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A025609 Number of n-move rook paths on 8 X 8 board from given corner to adjacent corner. 3
0, 1, 6, 64, 720, 9136, 122016, 1673344, 23216640, 323773696, 4525272576, 63308468224, 886046453760, 12403017773056, 173632453287936, 2430795572936704, 34030785382318080, 476428879520137216, 6669991618287108096, 93379806486052470784, 1307316833784928665600 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Paths are not required to be self-avoiding. - Andrew Howroyd, Nov 05 2019

LINKS

Andrew Howroyd, Table of n, a(n) for n = 0..200

Index entries for linear recurrences with constant coefficients, signature (18,-44,-168).

FORMULA

G.f.: x*(1 - 12*x)/((1 + 2*x)*(1 - 6*x)*(1 - 14*x)).

a(n) = 18*a(n-1) - 44*a(n-2) - 168*a(n-3) for n >= 3.

MATHEMATICA

CoefficientList[ Series[(x - 12 x^2)/((1 + 2 x) (1 - 6 x) (1 - 14 x)), {x, 0, 16}], x]

PROG

(PARI) concat([0], Vec((1 - 12*x)/((1 + 2*x)*(1 - 6*x)*(1 - 14*x)) + O(x^20)))

CROSSREFS

Cf. A025607, A025608.

Sequence in context: A237357 A230282 A186668 * A309186 A156887 A239847

Adjacent sequences:  A025606 A025607 A025608 * A025610 A025611 A025612

KEYWORD

nonn,walk

AUTHOR

David W. Wilson

EXTENSIONS

Terms a(17) and beyond from Andrew Howroyd, Nov 05 2019

STATUS

approved

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Last modified August 18 09:56 EDT 2022. Contains 356204 sequences. (Running on oeis4.)